Merryl’s pretty good bet: Bill Thompson (r.) isn’t leading in the polls now — but still stands a very strong chance of becoming mayor. Photo: Paul Martinka

The most powerful New Yorker in public education has just sent a message to the United Federation of Teachers: Back Bill Thompson for mayor in 2013.

How else to interpret last week’s announcement by Merryl Tisch, the state Board of Regents chancellor, that she’ll co-chair Thompson’s seemingly moribund mayoral campaign?

That is, she’s not just endorsing Thompson’s candidacy — but also actively enlisting in the undertaking.

This is just breathtaking, coming from the person responsible for oversight of all education policy in the Empire State — public and private, pre-K to post-grad, and everything in between.

In between, of course, includes teacher-evaluation policies, charter schools, the future of mayoral control of New York City’s 1.1-million-pupil public-school system — all items of critical interest to the UFT, an organization with outsized influence in municipal politics.

To put it mildly.

So Tisch says jump. Anybody doubt that the UFT will at least consider a hop and a skip?

Particularly since Tisch herself is the (some would say distressingly malleable) protégé of Assembly Speaker Sheldon Silver — a friend from the duo’s childhood days on the Lower East Side and the most transactional politician in New York’s ethically checkered recent history, as well as a teachers-union tool of long standing.

Who, by virtue of New York’s arcane process for filling the post, was able to anoint Tisch chancellor in the first place.

A little circular? Obviously.

A conflict of interest? Not according to Tisch.

“We set educational policy for the state,” she said last week. “We do not run the city’s school system.”

Artfully put, but highly misleading. Tisch and the Regents have direct control over the state Education Department, which in turn controls the city schools so tightly that the distinction really is, well, academic.

Certainly Tisch’s endorsement won’t be lost on the UFT.

What’s amazing is that this thoroughly obvious conflict of interest seems to be so totally lost on Tisch.

As for Thompson, well, who can blame a man for picking up found money — and a lot of it, given Tisch’s well-founded reputation as a political fund-raiser?

Certainly the addition of Tisch fits into the Thompson campaign game plan: Lay low, quietly court endorsements and raise money, then make a move at a strategic moment and hope that he’s one of the two Democratic candidates who survives for a post-primary runoff election.

True enough, public polls have Thompson stuck back with the also-rans, well behind City Council Speaker Christine Quinn. But polls can be peculiar, and the notion that the man who four years ago ended up just a stride behind Mike Bloomberg despite being outspent a gazillion-to-one is a second-tier candidate this time around is a little preposterous.

Thompson starts with a solid support base: his fellow black voters. And he has assiduously courted Brooklyn’s Orthodox Jews for decades — so successfully that The New York Times chronicled the relationship in wide-eyed wonder last February.

Moreover, he seems to already have the support of the Uniformed Firefighters Association. And he’s hard at work on the Patrolmen’s Benevolent Association — downplaying somewhat the public-safety side of that tricky equation while making it clear that the PBA’s bread-and-butter issues will be in good hands in a Thompson mayoralty. To unionists, that matters most.

All this adds up to a formidable coalition in the four-person primary campaign now under way. And it would be even more compelling if the execrable Anthony Weiner jumps in.

None of this is to predict anything, but merely to state what should be the obvious: Bill Thompson stands a more than passing chance of becoming the next mayor of New York City.

This would be good for him. But what about for Merryl Tisch — who’d then have to deal with the policy consequences of having been a pivotal presence in the campaign of the man who will be running the city’s public schools after Jan. 1?

Especially if the UFT climbs on the Thompson trolley?

Right now, the Tisch endorsement represents politics as usual in New York City — sordid, cynical and soaringly arrogant.

But if Thompson wins, Tisch will have handed herself an operational conflict of interest. That is, how can she credibly provide oversight — “set educational policy,” in her terms — for a Bill Thompson mayoralty?

Simply put, she can’t. But you can bet she’ll try.

Tisch is too smart not to understand all of this. Surely she does — and she went ahead and did it anyway. And she will persevere.

It speaks to her priorities — and thus to those of the current Board of Regents: